Algebra Examples

$\frac{- 3 x^{4}}{- 6 x^{2} + (- 3 x)}$

Step 1

Remove parentheses.

$\frac{- 3 x^{4}}{- 6 x^{2} - 3 x}$

Step 2

Factor $3 x$ out of $- 6 x^{2} - 3 x$ .

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Step 2.1

Factor $3 x$ out of $- 6 x^{2}$ .

$\frac{- 3 x^{4}}{3 x (- 2 x) - 3 x}$

Step 2.2

Factor $3 x$ out of $- 3 x$ .

$\frac{- 3 x^{4}}{3 x (- 2 x) + 3 x (- 1)}$

Step 2.3

Factor $3 x$ out of $3 x (- 2 x) + 3 x (- 1)$ .

$\frac{- 3 x^{4}}{3 x (- 2 x - 1)}$

$\frac{- 3 x^{4}}{3 x (- 2 x - 1)}$

Step 3

Cancel the common factor of $- 3$ and $3$ .

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Step 3.1

Factor $3$ out of $- 3 x^{4}$ .

$\frac{3 (- x^{4})}{3 x (- 2 x - 1)}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $3 x (- 2 x - 1)$ .

$\frac{3 (- x^{4})}{3 (x (- 2 x - 1))}$

Step 3.2.2

Cancel the common factor.

$\frac{3 (- x^{4})}{3 (x (- 2 x - 1))}$

Step 3.2.3

Rewrite the expression.

$\frac{- x^{4}}{x (- 2 x - 1)}$

$\frac{- x^{4}}{x (- 2 x - 1)}$

$\frac{- x^{4}}{x (- 2 x - 1)}$

Step 4

Cancel the common factor of $x^{4}$ and $x$ .

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Step 4.1

Factor $x$ out of $- x^{4}$ .

$\frac{x (- x^{3})}{x (- 2 x - 1)}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Cancel the common factor.

$\frac{x (- x^{3})}{x (- 2 x - 1)}$

Step 4.2.2

Rewrite the expression.

$\frac{- x^{3}}{- 2 x - 1}$

$\frac{- x^{3}}{- 2 x - 1}$

$\frac{- x^{3}}{- 2 x - 1}$

Step 5

Move the negative in front of the fraction.

$- \frac{x^{3}}{- 2 x - 1}$

Step 6

Factor $- 1$ out of $- 2 x$ .

$- \frac{x^{3}}{- (2 x) - 1}$

Step 7

Rewrite $- 1$ as $- 1 (1)$ .

$- \frac{x^{3}}{- (2 x) - 1 (1)}$

Step 8

Factor $- 1$ out of $- (2 x) - 1 (1)$ .

$- \frac{x^{3}}{- (2 x + 1)}$

Step 9

Simplify the expression.

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Step 9.1

Rewrite $- (2 x + 1)$ as $- 1 (2 x + 1)$ .

$- \frac{x^{3}}{- 1 (2 x + 1)}$

Step 9.2

Move the negative in front of the fraction.

$- - \frac{x^{3}}{2 x + 1}$

Step 9.3

Multiply $- 1$ by $- 1$ .

$1 \frac{x^{3}}{2 x + 1}$

Step 9.4

Multiply $\frac{x^{3}}{2 x + 1}$ by $1$ .

$\frac{x^{3}}{2 x + 1}$

$\frac{x^{3}}{2 x + 1}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$